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The interplay of BCS superconductivity and nontrivial band topology isexpected to give rise to opportunities for creating topologicalsuperconductors, achieved through pairing spin-filtered boundary modes viasuperconducting proximity effects. The thus-engineered topologicalsuperconductivity can, for example, facilitate the search for Majorana fermionquasiparticles in condensed matter systems. Here we report a first-principlesstudy of Mg$_2$Pb and predict that it should be a superconducting topologicalmaterial. The band topology of Mg$_2$Pb is identical to that of the archetypalquantum spin Hall insulator HgTe, while isostructural and isoelectronicMg$_2$Sn is topologically trivial; a trivial to topological transition ispredicted for Mg$_2$Sn$_{1-x}$Pb$_x$ for x~0.77. We propose thatMg$_2$Pb-Mg$_2$Sn quantum wells should generate robust spin-filtered edgecurrents in analogy to HgTe/CdTe quantum wells. In addition, our calculationspredict that Mg$_2$Pb should become superconducting upon electron doping.Therefore, Mg$_2$Pb is expected to provide a practical material platform forstudying emergent phenomena arising from the interplay of superconductivity andband topology.

Prediction of Nontrivial Band Topology and Superconductivity in Mg$_2$Pb